SETS is used for symbolic manipulation of set (or Boolean) equations, particularly the reduction of set equations by the application of set identities. It is a flexible and efficient tool for performing probabilistic risk analysis (PRA), vital area analysis, and common cause analysis. The equation manipulation capabilities of SETS can also be used to analyze noncoherent fault trees and determine prime implicants of Boolean functions, to verify circuit design implementation, to determine minimum cost fire protection requirements for nuclear reactor plants, to obtain solutions to combinatorial optimization problems with Boolean constraints, and to determine the susceptibility of a facility to unauthorized access through nullification of sensors in its protection system.

The SETS program is used to read, interpret,
and execute the statements of a SETS user program which is an
algorithm that specifies the particular manipulations to be
performed and the order in which they are to occur.

Any properly
formed set equation involving the set operations of union,
intersection, and complement is acceptable for processing by the
SETS program. Restrictions on the size of a set equation that can
be processed are not absolute but rather are related to the number
of terms in the disjunctive normal form of the equation, the
number of literals in the equation, etc. Nevertheless, set
equations involving thousands and even hundreds of thousands of
terms can be processed successfully.

Running time varies with respect to the particular set equations being processed and the symbolic manipulations being performed. Although no general rule for predicting run time is known, the reduction (expansion, simplification, and factorization) of a set equation usually requires more run time than other manipulations, and this time tends to increase as the number of terms in the disjunctive normal form of the set equation increases. NESC executed the SETS and FTD sample problem in 20 CP seconds on a CDC CYBER175. The SEP and FTD sample problems required 4 CP seconds and 1 CP second, respectively. The FTD sample problem was executed without plotting.

NESC0623/02

NEA-DB executed the test cases for the different programs contained in this package on CDC CYBER 740. The following CPU times were required: SETS - 122 seconds; SEP - 24 seconds; FTD - 4 seconds.

The SETS program is an
interpretive program used to execute the statements of a SETS user
program. The SETS user program provides the user with a flexible
capability for achieving the symbolic manipulation of set
equations.

Two auxiliary programs, SEP and FTD, are included. SEP performs the quantitative analysis of reduced Boolean equations (minimal cut sets) produced by SETS. The user can manipulate and evaluate the equations to find the probability of occurrence of any desired event and to produce an importance ranking of the terms and events in an equation. FTD is a fault tree drawing program which uses the proprietary ISSCO DISSPLA graphics software to produce an annotated drawing of a fault tree processed by SETS. The DISSPLA routines are not included.

SETS
must be compiled with optimization level of 0 or 1. Full optimization (OPT=2) produces compiler table overflows.
A substantial reprogramming effort would be required to convert the SETS program to a machine that is not compatible with the CDC6600 due to the extensive use of masking instructions and the packing of data within the 60-bit word structure.